# Mathematical Sciences Research Institute

Home » Recent Results in Nonlinear Elliptic Equations and their Interactions with Geometry

# Workshop

Recent Results in Nonlinear Elliptic Equations and their Interactions with Geometry October 31, 2005 - November 04, 2005
 Registration Deadline: September 25, 2005 about 9 years ago July 31, 2005 over 9 years ago
Organizers Frank Pacard, Neil Trudinger and Paul Yang
Speaker(s)

## Show List of Speakers

Description

This workshop will focus on recent developments in nonlinear elliptic equations and their interactions with differential geometry, Riemannian geometry and complex geometry. Topics will include the study of fully nonlinear elliptic problems which arise for example in the study of hessian equations for hypersurfaces, in complex Kahler geometry or in the prescription of the k-th symmetric functions of the eigenvalues of the Schouten tensor in conformal geometry and its analogue in CR geometry. It will also include the analysis of higher order elliptic equations which arise in affine geometry and conformal geometry. Lecture Schedule with Talk Abstracts SCHEDULE Monday, October 31 9:30 – 10:30 Gang Tian (Princeton Univ.), "Curvature estimate for 4-dimensional Einstein equation" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 Xiuxiong Chen (Univ. of Wisconsin), "On the Calabi functional in Kahler manifold" 12:00 – 1:00 Jeff Viaclovsky (MIT), “Volume Growth, Curvature Decay, and Critical Metrics” 1:00 – 2:30 Lunch 2:30 – 3:30 Xavier Cabre (ICREA-Univ. Politecnica Catalunya), "Regularity of radial minimizers and extremal radial solutions of semilinear elliptic equations" 3:30 – 4:00 Travel to 60 Evans Hall, UCB 4:10 – 5:10 (At 60 Evans Hall, UCB) Cristian Gutierrez (Temple University), “The Monge-Ampere equation: Overview and Recent Results” Tuesday, November 1 9:30 – 10:30 Richard Schoen (Stanford University), "Blowup issues for the Yamabe equation on high dimensional manifolds" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 Simon Brendle (Stanford University), "Global convergence of the Yamabe flow in dimension 6 and higher" 12:00 – 1:00 Olivier Druet (ENS Lyons), “The prescribed scalar curvature problem” 1:00 – 2:30 Lunch 2:30 – 3:30 Bernd Amman (Univ. Nancy), "The first Dirac eigenvalue in a conformal class" 3:30 – 4:00 Afternoon Tea – Sixth Floor 4:00 – 5:00 Xiaohua Zhu (Beijing University), “Kahler-Ricci flow and certain complex Monge-Ampere equation" Wednesday, November 2 9:30 – 10:30 Gerhard Huisken (Max Planck Inst. f. Gravitationsphysik), "Rigidity inequalities via inverse mean curvature flow" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 J. Cheng (Academica Sinica, Taipei), "The mean curvature equation in Pseudohermitian geometry" 12:00 – 1:00 Sophie Chen (Princeton University), “Boundary Estimates for Some Fully Nonlinear PDEs and Applications to Conformal Geometry” 1:00 – 2:30 Lunch 2:30 – 3:30 Qing Han (Univ. of Notre Dame), “Smooth local isometric embedding of surfaces with Gauss curvature changing sign monotonically across a curve” 3:30 – 4:00 Afternoon Tea – Sixth Floor 4:00 – 5:00 Nassif Ghoussoub (Univ. of British Columbia), "Selfdual variational principles for PDEs and evolution equations" Thursday, November 3 9:30 – 10:30 Bruno Franchi (Univ. of Bologna), "Intrinsic submanifolds of Heisenberg group" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 Joel Spruck (Johns Hopkins Univ.), "Complete hypersurfaces of constant curvature in Hyperbolic space with prescribed asymptotic boundary" 12:00 – 1:00 Refe Mazzeo (Stanford University), “Einstein metrics and higher rank geometry” 1:00 – 2:30 Lunch 2:30 – 3:30 Brian White (Stanford University), "Getting a handle on the helicoid" 3:30 – 4:00 Afternoon Tea – Sixth Floor 4:00 – 5:00 Xujia Wang (Australian National Univ.), “Fully nonlinear partial differential equations and applications in geometry” Friday, November 4 9:30 – 10:30 Luis Caffarelli (Univ. of Texas, Austin), "On homogenization and rates of convergence for random fully nonlinear equations" 10:30 – 11:00 Morning Tea – Sixth Floor 11:00 – 12:00 Alice Chang (Princeton Univ.), "Conformal invariants associated with a smooth measure" 12:00 – 1:00 Rod Gover (Univ. of Auckland) “Conformal Laplacian operators and Q-curvature on Einstein manifolds” 1:00 – 2:30 Lunch 2:30 – 3:30 Jie Qing (UC Santa Cruz), "“On semi-linear conformally invariant PDE” 3:30 – 4:00 Afternoon Tea – Sixth Floor 4:00 – 5:00 Fengbo Hang (Princeton & Michigan State Univ.), “On the higher order Q curvature on the Sphere”

Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code 123MSRI. Our preferred rate is $139 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

## Show Visa/Immigration

Schedule
Oct 31, 2004
Sunday
 09:30 AM - 10:30 AM Curvature Estimate for 4-dimensional Einstein Equation. Gang Tian (Princeton University)
Oct 31, 2005
Monday
 11:00 AM - 12:00 PM On the Calabi Functional in Kahler Manifold Xiu-Xiong Chen 12:00 PM - 01:00 PM Volume Growth, Curvature Decay, and Critical Metrics Jeff Viaclovsky (University of Wisconsin) 02:30 PM - 03:30 PM Regularity of Radial Minimizers and Extremal Radial Solutions of Semilinear Elliptic Equations. Xavier Cabré (Polytechnical University of Cataluña (Barcelona))
Nov 01, 2005
Tuesday
 09:30 AM - 10:30 AM Blowup Issues for the Yamabe Equation on High Dimensional Manifolds. Richard Schoen (Stanford University) 11:00 AM - 12:00 PM Global Convergence of the Yamabe Flow in Dimension 6 and Higher. Simon Brendle (Stanford University) 12:00 PM - 01:00 PM The Prescribed Scalar Curvature Problem. Olivier Druet 02:30 PM - 03:30 PM The First Dirac Eigenvalue in a Conformal Class. Bernd Ammann 04:00 PM - 05:00 PM Kahler-Ricci Flow and Certain Complex Monge-Ampere Equation. Xiaohua Zhu
Nov 02, 2005
Wednesday
 09:30 AM - 10:30 AM Rigidity Inequalities Via Inverse Mean Curvature Flow. Gerhard Huisken (Math. Forschungsinstitut Oberwolfach) 11:00 AM - 12:00 PM The Mean Curvature Equation in Pseudohermitian Geometry. Jih-Hsin Cheng 12:00 PM - 01:00 PM Boundary Estimates for Some Fully Nonlinear PDEs and Applications to Conformal Geometry. Szu-yu Sophie Chen 02:30 PM - 03:30 PM Smooth Local Isometric Embedding of Surfaces with Gauss Curvature Changing Sign Monotonically Across a Curve. Qing Han 04:00 PM - 05:00 PM Selfdual Variational Principles for PDEs and Evolution Equations. Nassif Ghoussoub (University of British Columbia)
Nov 03, 2005
Thursday
 09:30 AM - 10:30 AM On Semi-linear Conformally Invariant PDE. Jie Qing (University of California, Santa Cruz) 11:00 AM - 12:00 PM Complete Hypersurfaces of Constant Curvature in Hyperbolic Space with Prescribed Asymptotic Boundary. Joel Spruck (Johns Hopkins University) 12:00 PM - 01:00 PM Einstein Metrics and Higher Rank Geometry. Rafe Mazzeo (Stanford University) 02:30 PM - 03:30 PM Getting a Handle on the Helicord. Brian White 04:00 PM - 05:00 PM Fully Nonlinear Partial Differential Equations and Applications in Geometry. Xu-Jia Wang (Australian National University)
Nov 04, 2005
Friday
 11:00 AM - 12:00 PM Conformal Invariants Associated with a Smooth Measure. Sun-Yung Alice Chang (Princeton University) 12:00 PM - 01:00 PM Conformal Laplacian Operators and Q-curvature on Einstein Manifolds. Ashwin Gover 02:30 PM - 03:30 PM Intrinsic Submanifolds of Heisenberg Group. Bruno Franchi 04:00 PM - 05:00 PM On the Higher Order Q Curvature on the Sphere. Fengbo Hang